If upon retirement in 20 years Greg plans to invest 800,000 in a fund that earns 4 percent, What is the maximum annual withdrawal he can make over the following 15 years
To calculate the maximum annual withdrawal that Greg can make over the next 15 years, we need to use the concept of future value of an investment.
The future value (FV) of an investment can be calculated using the formula:
FV = PV * (1 + r)^n
Where:
PV = Present Value (initial investment)
r = interest rate (expressed as a decimal)
n = number of compounding periods (years)
In this case, the present value (PV) is $800,000, the interest rate (r) is 4% (or 0.04), and the number of compounding periods (n) is 20 years.
Plugging these values into the formula, we have:
FV = $800,000 * (1 + 0.04)^20
FV = $800,000 * (1.04)^20
FV ≈ $1,491,824.47
So, after 20 years, Greg's investment will grow to approximately $1,491,824.47.
Now, we can calculate the maximum annual withdrawal Greg can make over the next 15 years using the concept of annuity.
An annuity is a series of equal periodic payments. In this case, Greg plans to make equal annual withdrawals over 15 years.
The annual withdrawal formula for an annuity is:
Withdrawal = FV * (r / (1 - (1 + r)^-n))
Where:
Withdrawal = Annual withdrawal amount
FV = Future Value
r = interest rate (expressed as a decimal)
n = number of compounding periods (years)
Plugging in the values, we have:
Withdrawal = $1,491,824.47 * (0.04 / (1 - (1 + 0.04)^-15))
Withdrawal ≈ $133,749.85
Therefore, the maximum annual withdrawal Greg can make over the next 15 years is approximately $133,749.85.
To calculate the maximum annual withdrawal Greg can make over the following 15 years, we need to consider the concept of annuity. An annuity is a series of equal periodic payments, usually made at regular intervals.
We can use the formula for the present value of an annuity to solve this problem:
PVA = PMT * (1 - (1 + r)^(-n)) / r
where:
PVA = Present Value of the Annuity (the initial investment)
PMT = Payment per period (annual withdrawal)
r = Interest rate per period (4% or 0.04)
n = Number of periods (15 years)
After rearranging the formula, we get:
PMT = PVA * r / (1 - (1 + r)^(-n))
Now we can plug in the values:
PVA = $800,000
r = 0.04
n = 15
PMT = $800,000 * 0.04 / (1 - (1 + 0.04)^(-15))
After calculating this equation, the maximum annual withdrawal Greg can make over the following 15 years is approximately $72,607.79.